Homomorphisms of product semigroups
Let \(S_1, S_2, \ldots, S_N\) and \(R\) denote semigroups, and \(F : S_1 \times \cdots \times S_N \to R\) be a homomorphism. The author finds sufficient conditions for existence and uniqueness of decompositions of \(F\) as \(F = F_1 \otimes \cdots \otimes F_N\), where \(F_n : S_n \to R\) is a homomorphism for \(n = 1, \ldots, N\). Explicit formulas and properties of the composing homomorphisms \(F_1, \ldots, F_N\) are given. He also applies the theory to some interesting examples. In addition, he studies additive and multiplicative functions on a product of subsemigroups of \(\mathbb{N}\).
scientific article; zbMATH DE number 7468845
scientific article